2018-04-09

Hawking radiation, Gaussians

At lunch time, Matt Kleban (NYU) gave a nice overview of the simplest arguments that black holes must radiate. It was a memorial, of sorts, for Stephen Hawking. Fundamentally, the argument is that if GR is to be consistent with quantum mechanics, then you must have black-hole radiation. That argument is good and sensible, but it is certainly theoretically prejudiced, since it confidently predicts something that will never be observed, and by privileging one part of theory over another. In the discussion afterwards, we learned that GR people tend to think that black holes obviously destroy information, whereas particle physicists tend to think that information will be preserved by some heretofore unknown mechanism. That's interesting, and highlights how socially constructed some aspects of theory might be. But I learned a lot and loved the talk and the discussion. Kleban is a very deep person and a great colleague.

Earlier in the day, I got challenged on a claim that the prior prediction for a snapshot of the amplitude of one mode of a Gaussian-driven damped, harmonic oscillator would be zero-mean and Gaussian. Not the squared amplitude but the straight linear amplitude of the sinusoid with a particular phase. That rattled around in my head all day. Late in the day, I think I have a good argument: Every linear projection of a Gaussian process onto any basis function or anything else (so long as it is a linear function of the Gaussian-process data) will be Gaussian-distributed.